In February 1976, the play premiered at the Direct Theatre in New York City. David Dukes was set to play the part of Richard Tammurai, but left before rehearsals ended to replace John Wood in the Broadway play Travesties. In May, 1976, Titanic was moved off Broadway to the Van Dam Theater.

Titanic opens in the Titanic's dining room, where the Tammurais (Richard, Victoria, and their son Teddy) are seated. Pondering why they haven't been seated at the captain's table, Richard suggests that the "snub" may be a result of Victoria's less-than-noble past growing up on a pig farm in Indiana. Victoria in turn announces that she wants a divorce and further reveals that Teddy is not Richard's natural son, which prompts Richard to claim that their unseen daughter Annabella is not Victoria's natural daughter. From here, there is a comedic blur between three characters: Annabella, Harriet Lindsey, and Lidia, the latter of whom is confusingly (but amusingly) the captain's daughter...or is she?

With Victoria and Richard at odds, Lidia—who keeps and feeds a variety of animals in her vagina—befriends Teddy and coerces him into non-consensual bondage scenarios. Meanwhile, Victoria begins a lurid affair with the passionate captain while Richard ravenously pursues and humiliates Higgins, a young sailor. On several occasions, it appears that the vessel has struck that fabled iceberg and is sinking (a fate Annabella, Harriet/Lidia desperately desires), but the sounds of catastrophe are always followed by an announcement that it was merely the captain's wife broadcasting from a sound effects record—a practical joke that ultimately prompts the captain to execute his wife. Following her funeral, the characters decide a wedding is in order—Victoria will marry Annabella/Harriet Lindsey, and Richard will marry Teddy (who he has by now begun to call Dorothy). In the final scene, we return to the Titanic's dining room where Teddy and Annabella/Harriet/Lidia exact deadly revenge on Richard and Victoria, just before it appears once more that the ship has struck an iceberg...but has it?